August 25, 2011

Relationship between SST and Atmospheric Temperatures, and how this affects feedback estimates

In my previous attempts to calculate feedbacks, I’ve found that typically it is the satellite temperature indices (the lower troposphere temperatures) that give the highest correlation. There are some good reasons to think that this should be the case – for example, I’ve been working with the radiative kernels recently, and if I recall correctly some 85% of the temperature feedback response comes from the layers of the atmosphere rather than the surface.

In a recent discussion at the Air Vent, TTCA brings up an interesting point. Basically, if the bulk of the feedback response is due to atmospheric temperature changes, then the regressions must be performed against those. The “regression” method I’m referring to here is simply that originally pioneered by FG06 and discussed more here. Of course, if the surface temperature variations and atmospheric temperature variations are close to one another in time, then the feedback response will be near instantaneous with the surface temperatures as well, and we should be fine. I’ve decided to take a closer look within this post.

My script and data are available here. The script is sort of a hodge podge of stuff, as is the post itself.

First, a quick look at the different temperature series anomalies (relative to the 2000-2010 baseline):

Now here’s a look at the correlations (r^2 values) between the various indices:

As should be clear, the satellite temperatures (UAH and RSS) correlate very well with one another, and the surface temperatures (GISS and HadCRUT) also show fairly strong correlation. Clearly, the same “types” (surface vs. LTT) of temperatures correlate better with each other than with those of the other type. This makes sense, but as we’ll see, one reason is because 70% of the surface is the sea surface, and atmospheric temperatures actually lag sea surface temperatures by 1-2 months.

The two SST indices I’ll be using here are HadSST2 (from CRU website) and Reynolds (I believe this is the satellite data used for GISS, and I got it from Climate Explorer):

And here is how they correlate at different lag times with the atmospheric temperatures:

Clearly, the 0 lag time does not correlate as well with atmospheric temperatures as other lag times, which suggests that the atmospheric temperatures respond to sea surface temperatures a few months later, which in turn means that using instantaneous surface temperatures to estimate feedbacks is going to decorrelate our results even further.

First, a quick look at our feedback estimate using RSS LTT. Here I am using the CERES NET TOA flux observations (N) from my cloud feedback posts, and am estimating the forcing (Q) as simply a linear change from 0 to 0.25 W/m^2 to represent the GHG increase over the period (same estimate used in Dessler10).

This 2.93 slope (W/m^2/K) feedback corresponds to a sensitivity of around ~1.3 C per doubling of CO2. Now, what happens if we simply use sea surface temperature (Reynolds in this case)?

We get no correlation, leading to a near-zero estimate the climate feedback and thus an extremely high climate sensitivity. But if we use the SST anomaly from two months earlier (the approximate amount of time for the temperature changes to dominate the lower troposphere), it is quite a different story:

A much better correlation (although not great), and once again a higher estimate of feedback. Obviously the r^2 is still not as high as either of the satellite indices, but this is to be expected if atmospheric temperatures are affected by more than simply the previous months’ SST.

Anyhow, here are the results of my runs:

Note that this does not deal with the issues from Spencer and Braswell (2010 or 2011) and Lindzen and Choi (2011) regarding forcings confounding the signal. In this case, we’re looking at a lagged time to calculate the feedback simply because that’s when the feedback will be occurring, due to the lag in atmospheric temperature response to sea surface changes.

Like this:

Related

One thing to keep in mind when calculating slopes from the atmospheric temps is that their variations are usually in sync (with a few months delay) with those of the surface, but much bigger. Currently my best estimate is that, averaged over the globe, a fluctuation of one degree at the surface results in a fluctuation of 1.3 degrees in the LT data. This is slightly higher than the value on average for models and long term trends (which aren’t amplified in the atmosphere, in contrast to fluctuations). Since the temps are essentially the denominator of the slope, larger temp variations means smaller absolute values of slopes. Since even though we are measuring feedback response to atmospheric change, our interest is in the surface’s temperature sensitivity, one needs to account for this enhanced variance. However, the exact way to account for this is sure to be subject to all sorts of controversy. My preferred method of just multiplying the coefficients by a conversion factor may be too simplistic.

Nice observations, Troy about the lag between SST and SAT/TLT. This illustrates, btw, the problem with the time resolution of the current data sets. You really need a finer resolution than one month (one day is probably overkill, 7 day averages would be about right).

It is possible to get daily LT anomalies from UAH (in addition to the Ch 5 AMSU data) covering the full length of the record. It’s at the UAH website, I recently plotted up the record, but didn’t save an image file.

Thinking about the cause of the lag between surface temperature and radiation may help you find more effective correlations: According to the K&T energy balance diagram, only about 10% (40 W/m2) of upward OLR emitted by the surface escapes directly to space (at a rate that should be proportional to surface temperature and blocked by CRF). About twice as much energy (80 W/m2) leaves the surface as the latent heat in water vapor, a form of energy that causes no emission to space. Only after water vapor condenses does it become sensible heat that can result in radiation. The residence time for water vapor in the atmosphere appears (Wikipedia) to be about 10 days, well short of the 1-2 months seen in lagged correlations. The rate of evaporation depends on both SST and wind speed. (Air immediately above the surface of the ocean is nearly saturated and evaporation is dramatically enhanced by turbulent mixing.) On the K&T diagram, about 20 W/m2 of energy leaves the surface of the earth by convection of sensible heat.
(These are surface energy balances. Higher in the atmosphere, there is less water vapor to convect, photons travel further, and these proportions change.

Once sensible heat is in the atmosphere, that doesn’t mean it can escape to space as radiation. Emission from greenhouse gases occurs mostly at wavelengths that are well absorbed by the greenhouse gases that emitted those photons. A photon emitted by a CO2 or water near the surface of the earth may be much more likely to result in energy escaping to space if that photon is emitted downward (where it can be absorbed by the surface and re-emitted to space through the atmospheric window) than if it is emitted upward (where is it likely to be absorbed before it reaches space). A chain of absorptions and emissions may be needed and the energy will be observed as sensible heat/temperature of the atmosphere at different altitudes

Energy emitted at different wavelengths from different altitudes responds on different time scales. If you look only at the atmospheric window, where the surface but not GHG’s emit, outgoing radiation should vary immediately with SST. This might allow you to separate the component of feedback with no lag from the component with lag. Emission at other wavelengths could be emitted with a lag that depends on how fast sensible heat anomalies rise from the surface through the atmosphere to altitudes where they can effectively emit radiation to space.

The r2 from current correlations is poor because everyone is relying on an oversimplified model for how energy escapes to space from the surface.

Thanks, Frank, I agree that it looks like we need a better model for tracking the escape of this energy, particularly when the lag is greater than a month. Looking at some combination of the surface (no lag) and TLT will probably be required when it comes to determining the total feedback response.

It seem to me that you have shown through this demonstration that a lagged regression is appropriate notwithstanding the LC / SB arguments. A lagged difference time series of standardized surface minus atomosphere would give some interesting insight (through an ARIMA fit) into a component of the noise playing into the surface / TOA flux regression. Wouldn’t the tropospheric amplification pointed out by TTCA ultimately be reflected (properly) in the calculation of Lambda?

I first smoothed all three with a three sigma gaussian filter. This makes the data more continuous. You analysis is quantised into one month intervals which limits the result to be 1 2 or 3.

I’ll post the awk script I used as a filter below.

The many causes of decorrelation are a key issue in determining climate sensitivity. Contrary to what many people _assume_ , these errors in the data do not produce a symmetrical uncertainly of which the OLS regression estimator (incorreclty called “slope”) may be deemed to be a rough middle of the road average.

ALL causes of decorrelation cause a reduced “slope”, and it’s not a case of a few percent.

Current naive OLS fits being called “climate feedback” maybe under estimated by a _factor_ or 2 or 3.

Regarding the lag months, as mentioned above, you can get the _daily_ ch.5 and satellite SST temperatures, and if I recall this was closer to the 2-3 months than the 0.25 months…let me see if I can whip up a script in the coming days to confirm this. Are you sure your gaussian filter is actually a good predictor of temperatures on a sub-monthly time scales?

I’m increasingly inclined to agree that the low sensitivity estimates using OLS with measurements are likely the result of the decorrelation for a variety of reasons.

I should have explained the image a bit. The Y label is incorrect. I’ll have to document this more fully since it was revealing. The close tracking of the two would suggest temperature causing a change in CO2 rather than an accumulative warming due to excess greenhouse effect.

I was comparing various temp records to Muana Loa CO2 concentrations. To align the various datasets I had to back shift UAH by 0.25 years. That’s the point I intended to show.

troyca, I put up another post again with links. It disappeared when I hit “post comment”
I don’t know what is wrong.
Send me an email and I will repy with the post which I have saved in a MSWord file.
keep strong
cementafriend

The following is the post from cementafriend that for some reason WordPress kept eating, and he sent me via e-mail:
——————————————-

“@troyca , Not sure of the post time -it would have been am Oct 2 by your time. I hit the reply after Frank’s post, I think it came up with awaiting moderation. Unfortunately, I did not keep a copy. I will this time.

Is Trenberth’s lack of correction or withdrawal of his Global Heat Balance papers scientific fraud? I take the view that Trenberth does not understand heat & mass transfer (which is a chemical engineering discipline based on empirical evidence and measurement) or thermodynamics and he has no adequate explanation. However, it is not ethical or for that matter honest to dismiss measurements in favour of his wild assumptions particularly the creation of energy out of nothing.